Question

Which of the following is not a quadratic equation? 
A. x²-2x= (-2)(3-x)
B. x³-4x²-x+1=(x-2)³
C. x²+3x+1=(x-2)²
D. x²+1=x(1-x)​

Answer 1

Answer:

b.understood or not please tell

Answer 2

$A.\: Given \: x^{2} - 2x = (-2) (3-x)$

$\implies x^{2} - 2x = -6 + 2x$

$\implies x^{2} - 2x + 6 - 2x = 0$

$\implies x^{2} - 4x + 6 = 0$

$\blue{ It \: is \: in \:the \: form \: of }\\\blue{ax^{2} + bx + c = 0 }$

$\green{\therefore The \: given \: equation \: is \: a} \\\green {quadratic \: equation }$

$B. \: Given \: x^{3} - 4x^{2} - x + 1 = ( x - 2 )^{3}$

$\implies x^{3} - 4x^{2} - x + 1 = x^{3} - 3 \times x^{2} \times 2 + 3 \times x \times 2^{2} - 2^{3}$

$\implies x^{3} - 4x^{2} - x + 1 = x^{3} - 6x^{2} + 12x - 8$

$\implies x^{3} - 4x^{2} - x + 1 - x^{3} + 6x^{2} - 12x +8=0$

$\implies 2x^{2} -13x +9 = 0$

$\blue{ It \: is \: in \:the \: form \: of }\\\blue{ax^{2} + bx + c = 0 }$

$\green{\therefore The \: given \: equation \: is } \\\green {a\: quadratic \: equation }$

$C. \: Given \:x^{2} +3x+1 = (x-2)^{2}$

$\implies x^{2} + 3x + 1 = x^{2} - 2 \times x \times 2 + 2^{2}$

$\implies x^{2} + 3x + 1 = x^{2} - 4x + 4$

$\implies x^{2} + 3x + 1 - x^{2} + 4x - 4= 0$

$\implies 7x - 3 = 0$

$\red{ It \: is \:not \: in \:the \: form \: of }\\\blue{ax^{2} + bx + c = 0 }$

$\red{\therefore The \: given \: equation \: is } \\\green {not \: a \: quadratic \: equation }$

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